Invasive treatment methods are known for the stabilization of spinal columns in which bone bridges are made to grow between adjacent vertebral bodies using implants. Stiffening fusions of the adjacent vertebrae result through the bone bridges. In addition to stiffening operations of this kind a treatment method for stabilizing by means of an implant system is also known in which no fusion arises, but rather a mobility is preserved between adjacent vertebrae. This implant system comprises pedicle screws and intervertebral support elements which are implanted during the operation from the back. Each pedicle screw has a head which is formed as a ring. In each case two pedicle screws are screwed in a vertebral body through the pedicle passages of the vertebra. The support elements are secured at the screw heads. Two support elements which are arranged in parallel between adjacent vertebrae form a dynamic supporting of these vertebrae. The vertebrae—with the exception of the lowermost lumbar vertebra—can in each case also be connected at the same pedicle screws to an upwardly and a downwardly adjacent vertebra through two pairs of support elements. Each support element consists of a piece of a cable-like band and a cylindrical support body which is elastically yielding. A rigid material can also be used for individual support bodies in order to stiffen the spinal column at individual locations. The band is drawn in an axial lumen of the support body. The intervertebral support elements are secured at the pedicle screws using the band. In this the bands must be drawn through the ring heads. The drawing in of the band is an operation step which is difficult to carry out.